5.4 Numerical predictions of GW emission

The GW emission from the collapse of Population III stars has been investigated by Fryer and
collaborators (Fryer, Woosley, and Heger [96], FHH [86], and Fryer, Holz, Hughes, and Warren [88]). The
collapse simulations of Fryer, Woosley, and Heger again started with rotating collapse progenitors that had
been evolved with a stellar evolution code [107]. The initial models used by the evolution code were in rigid
rotation with a surface ratio of centrifugal to gravitational forces of 20% (this ratio is seen in current
observations of O stars).

The results of Fryer, Woosley, and Heger suggest that the collapse remnant (prior to black hole
formation) is susceptible to the development of a secular bar-mode instability. However, at , the GW
emission would be redshifted out of LIGO-II’s frequency range. At , , with a
corresponding frequency of [86, 88]. Even if such a signal persists for a hundred cycles, it
probably would be undetectable by LIGO-II. Note that these signal strengths are orders of
magnitude lower than the qualitative estimates of signal strength given in Carr, Bond, and
Arnett [47].

LIGO-II may be able to detect the GW emission from binary clumps formed via a fragmentation
instability. If such a signal is emitted at and persists for 10 cycles, would be , over a
frequency range of [86, 88]. The likelihood of the development of a fragmentation instability
is diminished by the fact that the off-center density maxima present in the simulations of Fryer, Woosley,
and Heger are not very pronounced.

The “ring-down” of the black hole remnant will likely be strong because Fryer, Woosley, and Heger
observe a high accretion rate after collapse. FHH estimate that for a source located at , the GWs
would be redshifted out of LIGO-II’s bandwidth. However, for a source at , and
the frequency range is . This signal may be marginally detectable with LIGO-II (see
Figure 2).